When using an automatic programming apparatus configured to receive an input of machining unit data that is used for performing partial machining and includes data indicating a machining region shape, a machining method, tools to be used, and machining conditions and to generate control command information to operate a machine tool based on the input machining unit data, a chamfering process is a process to remove a corner portion of a boundary part in which planes positioned adjacent to each other intersect each other, and the shape of a chamfered part may be complicated when the target of a chamfering process is a boundary part formed by two curved planes. For this reason, the machining is normally performed manually or while employing an automatic programming apparatus, according to a Numerical Control (NC) computer program (hereinafter, “NC program”) that is prepared, in advance, for performing chamfering processes (see, for example, Patent Document 1). In most situations, a chamfering process is sufficient so long as the corner portion is removed; it is therefore rare that a high level of precision is required. Further, because the method for performing a chamfering process varies depending on the part to which the chamfering process is to be applied and the material, the method for instructing the chamfering process may also vary according to the chamfering method to be used.